Variational ground states of the two-dimensional Hubbard model

TL;DR

This paper uses variational methods to study the ground states of the 2D Hubbard model, revealing antiferromagnetism at half filling and d-wave superconductivity away from it, with results aligning well with recent numerical studies.

Contribution

It introduces a variational ansatz that captures key ground state properties of the 2D Hubbard model and compares favorably with advanced numerical methods.

Findings

Antiferromagnetic order at half filling with reduced order parameter.

D-wave superconductivity appears away from half filling.

Variational gap parameters vary widely, but order parameters are more robust.

Abstract

Recent refinements of analytical and numerical methods have improved our understanding of the ground-state phase diagram of the two-dimensional (2D) Hubbard model. Here we focus on variational approaches, but comparisons with both Quantum Cluster and Gaussian Monte Carlo methods are also made. Our own ansatz leads to an antiferromagnetic ground state at half filling with a slightly reduced staggered order parameter (as compared to simple mean-field theory). Away from half filling, we find d-wave superconductivity, but confined to densities where the Fermi surface passes through the antiferromagnetic zone boundary (if hopping between both nearest-neighbour and next-nearest-neighbour sites is considered). Our results agree surprisingly well with recent numerical studies using the Quantum Cluster method. An interesting trend is found by comparing gap parameters (antiferromagnetic or superconducting) obtained with different variational wave functions. They vary by an order of magnitude and thus cannot be taken as a characteristic energy scale. In contrast, the order parameter is much less sensitive to the degree of sophistication of the variational schemes, at least at and near half filling.